Inclusion problems in ordered topological vector spaces and applications
The author studies the existence of minimal and maximal solutions of inclusion problems in ordered topological vector spaces (TVS) of the form \(Lu\in Nu\) where \(L\) is a single-valued map from a partially ordered set \(V\) onto a nonempty subset \(P\) of an ordered TVS \(X\) (satisfying some order-theoretic assumptions) and \(N\) is a set-valued map on \(V\) admitting nonempty values in \(X\). The obtained results are then applied to some more concrete problems in reflexive lattice-ordered Banach spaces and, in particular, to some functional parabolic initial-boundary and elliptic boundary value problems for partial differential inclusions in order to get minimal and maximal weak solutions with respect to the natural almost everywhere pointwise order that is introduced in appropriate Sobolev-type spaces.
scientific article; zbMATH DE number 2117729